Nonlocal Superposed Solutions II: Coupled Nonlinear Equations

TL;DR

This paper introduces new periodic and hyperbolic solutions for coupled nonlocal nonlinear Schrödinger and mKdV equations, demonstrating the extension of superposed solutions to coupled nonlocal nonlinear systems.

Contribution

It presents novel superposed solutions for coupled nonlocal nonlinear equations, expanding the understanding of solution structures in these systems.

Findings

Derived new periodic and hyperbolic solutions

Showed superposition principle applies to coupled nonlocal equations

Extended solution methods to coupled nonlocal nonlinear systems

Abstract

We obtain novel periodic as well as hyperbolic solutions of an Ablowitz-Musslimani variant of the coupled nonlocal, nonlinear Schr\"odinger equation (NLS) as well as a coupled nonlocal modified Korteweg-de Vries (mKdV) equation which can be re-expressed as a linear superposition of the sum or the difference of two hyperbolic or two periodic kink or pulse solutions. Besides, we also discuss some of the other solutions admitted by these coupled equations. These results demonstrate that the notion of the superposed solutions extends to the coupled nonlocal nonlinear equations as well.